mathematics

Letters to a German Princess

Letters to a German Princess is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Letters to a German Princess rather than just read about it. In short: Letters to a German Princess, On Different Subjects in Physics and Philosophy (French: Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie) were a series of 234 letters written by the mathematician Leonhard Euler between 1760 and 1762 addressed to Friederike Charlotte of Brandenburg-Schwedt and her younger sister Louise. Contents Euler started the first letter with an explanation of t…

Key takeaways

Letters to a German Princess belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Letters to a German Princess to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Letters to a German Princess from memory before moving on to harder problems.

Reference excerpt

Letters to a German Princess, On Different Subjects in Physics and Philosophy (French: Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie) were a series of 234 letters written by the mathematician Leonhard Euler between 1760 and 1762 addressed to Friederike Charlotte of Brandenburg-Schwedt and her younger sister Louise.

Contents Euler started the first letter with an explanation of the concept of "size". Starting with the definition of a foot, he defined the mile and the diameter of the earth as a unit in terms of foot and then calculated the distance of the planets of the Solar System in terms of the diameter of the earth.

Publication The first two volumes of the 234 letters originally written in French appeared in print in Saint Petersburg in 1768 and the third in Frankfurt in 1774. The letters were later reprinted in Paris with the first volume in 1787, the second in 1788 and the third in 1789. The publication of the book was supported by Empress Catherine II with her personally writing to Count Vorontsov in January 1766:

I am certain that the academy will be resurrected from its ashes by such an important acquisition, and congratulate myself in advance in having restored this great man to Russia. Russian translation of the letters followed in Saint Petersburg by Euler's student Stepan Rumovsky between 1768 and 1774 in 3 volumes.

Translations The first English translation of the Letters were done by the Scottish minister Henry Hunter in 1795. Hunter targeted the translation at British women, believing that Euler intended to educate women through his work. The translation of Hunter was based on the 1787 Paris Edition, of Marquis de Condorcet and Sylvestre François Lacroix. The translation differed from the original letters of Euler in its omission of "... the frequent, tiresome, courtly address of YOUR HIGHNESS". The Marquis de Condorcet's translation, made during the Age of Enlightenment, was notable for its omission of Euler's theological references which Condorcet found as "anathema" to teaching science and rationalism. Translations followed in other languages including Spanish (1798) which differed from the original book by a footnote describing the newly discovered planet Uranus. Subsequent German edition (1847), and French editions (1812 and 1829) were also noted for their reference to Uranus and four minor planets respectively.

See also On the Connexion of the Physical Sciences

References and notes

Attribution This article incorporates text from a publication now in the public domain: Lee, Sidney, ed. (1891). "Hunter, Henry". Dictionary of National Biography. Vol. 28. London: Smith, Elder & Co.

External links Letters on Different Subjects in Natural Philosophy, Volume 1 public domain audiobook at LibriVox

Illustrations

Worked examples

Example 1 — a first encounter with Letters to a German Princess

Start with the simplest possible case. Write down what Letters to a German Princess claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Letters to a German Princess before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Letters to a German Princess ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Letters to a German Princess

In research: Letters to a German Princess appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Letters to a German Princess in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Letters to a German Princess is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1760s works, Collections of letters, Mathematics books, so understanding it makes those chapters shorter.
In everyday life: Look for Letters to a German Princess outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Letters to a German Princess in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Letters to a German Princess means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Letters to a German Princess out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Letters to a German Princess in simple terms?

Why does Letters to a German Princess matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Letters to a German Princess?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Letters to a German Princess.